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Chapter 7: Q. 25 (page 178)

The $100 k g$ block in FIGURE EX $7.25$ takes $6.0 s$ to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless.

Short Answer

Expert verified

The acceleration of the $2.0 k g$ blocks is $2.16 m / s^{2}$

Step by step solution

01

Given information

Mass of right block, $M = 100 k g$

Time taken $t = 6 s$

Distance moved $s = 1 m$

02

Explanation

Equation of motion for mass m

$T - m g = m a 鈥� 鈥� (1)$

Equation of motion for mass M:

$M g - T = M a 鈰� 鈰� (2)$

On adding equation $(1) and(2)$

$g (M - m) = a (M + m) m = \frac{M (g - a)}{(g + a)}$

Acceleration a can be calculated as follows.

localid="1649613906426" $s = u t + \frac{1}{2} a t^{2} u = 0 s = 1 m t = 6 s 1 m = 0 + \frac{1}{2} (a) {(6 s)}^{2} a = \frac{2}{36} m / s^{2} a = 0.055 m / s^{2} m = \frac{(100 k g) (9.8 m / s^{2} - 0.055 m / s^{2})}{(9.8 m / s^{2}) + (0.055 m / s^{2})} m = 98.87 k g$

The mass of the block on the left side is $98.87 k g$

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Most popular questions from this chapter

A $2.0 k g$ rope hangs from the ceiling. What is the tension at the midpoint of the rope?

FIGURE $P 7.27$ shows a $6.0 N$ force pushing two gliders along an air track. The $200 g$ spring between the gliders is compressed. How much force does the spring exert on

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The spring is firmly attached to the gliders, and it does not sag.

The two blocks in FIGURE $P 7.34$ are sliding down the incline. What is the tension in the massless string?

The coefficient of static friction is $0.60$ between the two blocks in FIGURE $P 7.35$ . The coefficient of kinetic friction between the lower block and the floor is $0.20$ . Force $\overset{鈫�}{F}$ causes both blocks to cross a distance of $5.0 m$ , starting from rest. What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?

The block of massM inFIGURE $P 7.36$ slides on a frictionless surface. Find an expression for the tension in the string

See all solutions

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